You could try updating the URLs in the WP database itself. But be warned, if you take a wrong step, this could crash your site. And obviously, make a backup of any database before you attempt to manipulate it.
Use the developer tools in Firefox or Chrome or Safari to see the error with the specific images.
You may need to change the URL of media item on the post/page content to HTTPS. SearchRegEx is a good plugin to be able to search and replace through all pages, pages.
You may need to change to a relative path for images in CSS files i.e background-image: url(http://example.com/themes/wp-content/theme/images/image.jpg) to background-image: url(images/image.jpg)
3 You may need to improve to HTTP from absolute paths in php themes files, i.e change http://example.com/image.jpg to //example.com/image.jpg ; that will allow your resources to default to https.